SEO is the process of improving traffic to your website by making changes in structure, code, links or adding quality in search of getting your website to rank better in unpaid search results.
There are multiple ways of doing this.
When developing your website or getting it developed by a web designer/developer ensure your most important keywords are used. To rank higher quicker I would advise go for less competitive keywords. Once your website is popular,etc. move onto getting it to rank better on the harder more competitive keywords. Ensure when you post on other sites that you use these keywords and post links back to your site. Ensure keywords are used in your title of your website aswell as meta descriptions.
Content is by far the most important and highly rated technique used in SEO to rank better on Google and Bing. Ensure you create new and unique content daily or weekly but keep it consistent to ensure that Google or Bing picks this up and starts ranking your site better in search results. Remember: Google loves content above anything else.
Try and get links back to your website with anchor text of your keyword. This can be done by posting on forums with useful information, adding signatures with links back to your website, creating profiles on forums (old method), etc.
The best way however and the most rewarding is to build a blog or forum with good quality content and information that will be shared by 1000s of readers on the web. This obviously may take time but is something to start working on from day one.
Probably the most used technique used today is social media. Getting likes etc. in my opinion helps but is not what should be concentrated on. Create accounts on Google Plus, Facebook and Twitter and ensure that you post there often to keep interest and improve your brand for new visitors and current viewers. Keep on this and the reward can be great.